The tool to allow that is the unrolling of optimization algorithms [1]}.
The Primal-Dual net [2]}, shortened as PDNet, is derived when unrolling the Primal-Dual Hybrid Gradient optimization algorithm [3]} (also known as Chambolle-Pock algorithm).
A primal only version also exists, which does not use a k-space correction but simply computes the residual between the original measurements and the measurements associated with the image solution at a given unrolled iteration.
We use this version to avoid using a computationally expensive neural network in the k-space.
